数值微分

Chapter 5 to text the numerical method put forward carries on the numerical experiment, special two fractional differential equation problem within biologies carries on the test, the number result enunciation method is valid.

第五章对文中所提出的数值方法进行了数值试验，特别就计算生物学中的两个分数阶微分方程问题进行测试，数值结果表明方法是有效的。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

Then the explicit expression of it under exponential claims and the differential equation are obtained.Thus we discuss the effects of credit and debit interests on it through data analysis. Through the research of the mean,the moment generating function and the higher moments of discounted aggregate dividend payments,we discuss the optimal dividend payments problems.

而对于Gerber-Shiu函数的研究，则是通过随机过程及随机微分方程的知识得到它满足的积分-微分方程及边值问题，然后得到了它在指数索赔下的明确表达式以及Erlang(2)索赔下满足的微分方程，并通过数值分析得到贷款利息及存款利息对它的影响。

Differential Quadrature Method, one of numerical methods of solving boundary problem of differential equation is introduced in this paper. By using DQM, the dynamic stability of pipes conveying fluid and rectangular plates under the action of non-conservative force is studied. The main research work is as follows.

本文首先介绍了求解微分方程边值问题的一种数值方法—微分求积法，然后采用微分求积法分别对输流管道和非保守矩形薄板的稳定性问题进行了分析研究，具体有如下三方面的研究内容。

By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations, the stability criteria of the methods are derived.

通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则。

Let the obtained modality parameters be substituted into the coupling vibration partial differential equation and transform the complex partial differential equation into the variable coefficient nonlinear or...

把所得模态参数代入耦合振动偏微分方程中，将复杂的偏微分方程转化为变系数非线性常微分方程组，用Runge-Kutta方法获得方程的数值解。

After the brief retrospect of spectral methods applied to get the numerical solutions of partial differential equations, the Walsh spectral methods are extensively studied. A new method of designing the "derivate operator" and a new Walsh spectral method based on quasi-Walsh order are proposed, which primarily prove the special uses of it.

回顾了数值求解偏微分方程的谱方法，比较深入地考察了数值求解偏微分方程的Walsh谱方法，提出了一种新的设计"求导算子"的方法，基于这样设计出来的"求导算子"，提出了一种新的基于类Walsh序的Walsh函数的Walsh谱方法，初步验证了这种序的特殊价值。

The numerical calculation commonly used for the Delphi process more than 100, including solutions of linear algebraic equations, interpolation, numerical integration, special, function approximation, eigenvalue problems, data fitting equation Root and solve nonlinear equations, functions and the extreme optimization, statistical data description, Fourier transform spectra, solution of ordinary differential equations reconciliation partial differential equations.

本书共有数值计算中常用的Delphi子过程100多个，内容包括解线性代数方程组、插值、数值积分、特殊函数、函数逼近、特征值问题、数据拟合、方程求根和非线性方程组求解、函数的极值和最优化、数据的统计描述、傅里叶变换谱方法、解常微分方程组和解偏微分方程组。

It is proved that equilibrium solutions of this differential system are solutions to the complementarity problem and a numerical algorithm is given based on the numerical integration of the system of ordinary differential equations.

在一定条件下，证明了微分方程系统的平衡点是非线性互补问题的解并且基于一般微分方程系统的数值积分建立了一个数值算法。

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

为了研究两自由度机械手系统的动力学稳定性，基于拉格朗日方程给出了它的运动微分方程，并用扰动理论确定系统周期运动具有周期系数的扰动微分方程；根据F loquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析，并用数值方法研究了平衡点失稳后的倍周期分岔过程。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。